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2s - THE UNIVERSITY OF HONG KONG FACULTY OF BUSINESS AND...

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1 T HE U NIVERSITY OF H ONG K ONG F ACULTY OF B USINESS AND E CONOMICS FINA0301 CDE - D ERIVATIVES First Semester, 2009-2010 Tutorial 2 Problem Set Solution – Chapter 3 checkbld Practice Questions Question 1 A bull spread is created by buying the $30 put and selling the $35 put. This strategy gives rise to an initial cash inflow of $3. The outcome is as follows: Stock Price Payoff Profit S T 35 0 3 30 S T < 35 S T - 35 S T – 32 S T < 30 -5 -2 A bear spread is created by selling the $30 put and buying the $35 put. This strategy costs $3 initially. The outcome is as follows: Stock Price Payoff Profit S T 35 0 -3 30 S T < 35 35 - S T 32 - S T S T < 30 5 2 Question 2 The bull spread is created by buying a put with strike price K 1 and selling a put with strike price K 2 . The payoff is calculated as follows: Stock Price Range Payoff from Long Put Option Payoff from Short Put Option Total Payoff S T K 1 0 0 0 K 1 < S T < K 2 0 S T – K 2 - ( K 2 – S T ) S T K 1 K 1 – S T S T – K 2 - ( K 2 – K 1 )
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FINA0301 – Tutorial 2 Solution Mr. Clive Man Chung HO 2 Question 3 (i) Payoff: If we buy the index, we receive at the time of expiration T of the options simply S T . The payoffs of part (ii) are a little bit more complicated. If we deal with options and the maximum function, it is convenient to split the future values of the index into two regions: one where S T < K and another one where S T K . We then look at each region separately, and hope to be able to draw a conclusion when we look at the aggregate position. (ii) We have for the payoffs in (ii): Instrument S T < K= 950 S T K = 950 Get repayment of loan $931.37 ×1.02 = $950 $931.37 ×1.02 = $950 Long Call Option max ( S T - 950, 0) = 0 S T -950 Short Put Option - max (950 - S T , 0) 0 Total S T -1020 S T -1020
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FINA0301 – Tutorial 2 Solution Mr. Clive Man Chung HO 3 We now see that the total aggregate position only gives us S T , no matter what the final index value is the same payoff as in part (i). Our proof for the payoff equivalence is complete.
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